COVID-19 Math Tutoring

Transformative Tutoring remains open to help students through this unusual time. Without regular school work, this could be a great opportunity to begin preparing for the SAT or ACT (which are usually taken for practice in the spring of your junior year and then again in the fall of your senior year). We offer private one on one tutoring in person or via FaceTime or Zoom. Check our schedule to make an appointment.

March 17, 2020 – All K-12 schools in FL will remain closed until April 15th. All state FSA testing has been canceled for 2019-2020. All university campuses are closed through the end of the semester and students will do online learning. Schools may be asked to extend the school year to June 30. For seniors trying to qualify for Bright Futures it is not yet clear what accommodations are being made. Read more from the FL Department of Education here.

March 16, 2020 – Presently, the College Board has not changed the AP testing dates. The College Board offers late testing each year and it is likely that the late testing days will become the test days. Read the latest here.

March 16, 2020 – The College Board has announced that the May 2020 SAT has been completely canceled. Keep up to date with the latest SAT news here.

March 15, 2020 – ACT has postponed the April 4th test to June 13th. Read more here.

Perfect 800 on the SAT – Congratulations Carter!

Carter on the first day of 9th grade

We just got the official score from the College Board that Carter got a perfect 800 on the SAT math test. We are so proud of Carter for this outstanding accomplishment.

Use the Official SAT Practice Tests

Carter had taken the SAT at the start of 7th grade and scored a 760, so we knew he was going to do well, but we decided to not take any chances and have him do all of the official SAT practice tests, just to get his mind back into SAT mode. He did a great job as you can see below:

Practice Makes Perfect! - Carter's completed official SAT practice tests that helped him get his perfect 800 on the SAT math test in 9th grade.

Rewarding Hard Work Paid Off

Part of why Carter succeeded (and why some others do not) is that he was really motivated to do quality work on these practice tests. I offered him the following incentive plan, $5 for 80% (90% on packets 5-10) correct and $10 for perfect packets. Then, if he got a perfect score on the actual SAT test, I would double the total. Carter likes money just as much as most people that I’ve met, so he was highly motivated to do quality work. This is the component that I see lacking in so many students these days. They seem to be going through the motions. They don’t really want to do the work and do not push themselves to get every question correct, regardless of the how difficulty of the question. It’s sort of an “I’ll try harder next time” approach. Rewarding him for his tenacity on the practice problems is the key ingredient to making sure that he has the will, the skill and the experience to break apart any unusual question that appears on the actual test.

Why Younger Students Can Succeed When Older Students Sometimes Cannot

Some people are probably wondering why a 7th or 9th grader would be taking the SAT at all. There are several reasons. First, the 7th grade test was to qualify for talented youth programs like Duke TIP and Johns Hopkins CTY. The 9th grade test was based on what I was seeing every week in my tutoring center. Older students often have too many distractions and too much stress to actually perform at their best. Also, older students seem to forget a lot of what they learned in middle school (which to the surprise of many people is actually a sizable portion of what is on the SAT math test). Carter has a fantastic understanding of math, so I never worry that he will forget his middle school math, but I wanted to shelter him from some of the pressure that I see negatively affecting the older students.

Only time will tell if a perfect score in 9th grade will be a benefit or not, but for now we are celebrating his extraordinary achievement and could not be prouder of him! Congratulations Carter! You are amazing!

The Best AP Calculus Resources

Succeeding in AP Calculus takes work! If you are going to put in the work, make sure you are working smarter, not harder. Here are the best resources that I have found to help you be efficient and get great practice quickly. Of course, if you need tutoring in Osprey or via FaceTime/Computer, just schedule a tutoring session and we will be happy to help.

Studying for a AP Calculus Chapter Test

The files listed below are great for studying for a chapter test. They have all of the released problems from 1969 through 2012 categorized by topic. The saint who did this work will forever have my appreciation. First, open the “Table of Contents” file and look for the topic(s) that are on your chapter test. This will tell you what page numbers will contain relevant questions. Then, use the “Pages” file(s) to find the actual questions. For example, suppose your chapter test is on “Area Between Curves”, the Table of Contents says that ” Area Between Curves” can be found on pages 242-245, so open the “Pages 208-313” file and scroll to page 242 (page numbers are handwritten at the bottom of each page). Note that next to each question the year is written in pen, so the first “Area Between Curves” question is question #1 from the 1993 BC exam. Using the question number and year, then you can look up the correct answer.

For the 2020 exams, when school campuses were closed due to the Coronavirus, AP had a great series of “Live Lessons” on YouTube. They are available here: AB and BC. AP also released a series of practice problems coordinated with these live lessons. The practice problems are organized by topic and are available here: AB and BC. Because the 2020 test had only free response (FRQ) questions, there are not any multiple choice (MC) questions in this set of practice problems. Furthermore, because the 2020 test was open note and taken at home, it was designed specifically to minimize cheating and the problem style is highly concentrated on abstract functions and data in tables and graphs. As a result, these questions are not completely representative of what would normally appear on a chapter or final test, but they are still a great repository of AP style questions.

Studying for the AP Calculus Final Exam

The best way to study for the final exam or a mid-year mid-term is to do AP calculus questions in no particular order. The old sample exams are a great way to do this. The following items are great resources for studying for a final or mid-term.

AP Calculus Multiple Choice Questions 1969 – 1998

This is a great collection of older multiple choice problems for the AP Calculus AB or BC practice exams. Many of these questions (unaltered) appear in prep books and many of these questions seem to appear in later released tests as well. Although this is a great collection, it does not have the benefit of being quickly searched and sorted the way the spreadsheet does. Luckily, someone took the time to categorize the questions in this document. It isn’t very flashy, but it gets the job done! Of course, if you only have questions and no answers that is not help, so here is a document that includes all of the answers and solutions. It is a large file, so you might want to download one of these smaller files instead: AB and BC Answer Key (without solutions) or the BC Answer Key and Solutions.

Additional AP Calculus Practice Exams with Answers

Just looking for some AP Calculus practice problems in a random order? Here are several practice exams or sets of sample questions that have been released by the College Board in recent years:

Categorized AP Calculus Multiple Choice Questions

The categorized list of multiple choice AP Calculus problems from 1998 – 2012 for both AB and BC Calculus is by far the most organized resource that I have found. This spreadsheet is amazing because it lists 400 multiple choice questions by learning outcome, test date, question number and most importantly of all, links to every question with the answer and solution. These questions are all questions that have been released by the College Board, so you won’t find questions for every year because the College Board does not release questions every year, but the 400 questions in this spreadsheet will keep you pretty busy! Here are a few recommendations on how to best use this spreadsheet:

  • Sort the spreadsheet by “Learning Outcome” that will help all of the questions on the same topic listed together and will put them in the approximate order that you will study them throughout the year. The spreadsheet is currently sorted by “Learning Outcome.”
  • As needed, filter the spreadsheet by “Key Idea”. Even though the spreadsheet is sorted by “Learning Outcome”, sometimes a question includes multiple “Key Ideas” (and “Learning Outcomes”), so filtering can help find additional questions. Here is a picture showing how you might do that so you only see questions on “concavity”:
Filtering AP Calculus Multiple-Choice Questions By Key Idea
  • Once you have the questions organized, click on the link to the PDF file that includes question. This PDF also includes the solution at the bottom of the page, so you can quickly check your answer and perhaps learn additional techniques for solving the question.
  • If you get the question correct and it was easy for you, great, just close the PDF. However, if you struggled at all, you can click the Download icon and save the difficult questions onto your computer so that you can then re-do every challenging question over and over again until they become easy. Once a question becomes easy, move the PDF to your “Not Hard Anymore” folder. This will also allow you to have a nice set of difficult questions to review as you prepare for the final AP exam. You might create a folder structure that looks like this:
Organizing AP Calculus Multiple-Choice Questions
  • Add a column or two to the spreadsheet so you can make your own notes about each question. Perhaps you want to rate each question by difficulty or categorize them by what chapter you were studying.

Categorized AP Calculus Free Response Questions (FRQs)

Just like the invaluable categorized spreadsheet of multiple choice questions mentioned above, this spreadsheet is just as incredible, but it contains the AP Calculus Free Response Questions (FRQs) from 1998 to 2017. These questions are released by the College Board each year, so there are nearly 1,000 questions here!

Calculus Free Response Justifications

Answers to the AP Calculus FRQs are supposed to be short and sweet. Less is more when it comes to these answers. This is a comprehensive guideline for the best way to justify your answers. Memorize the wording in these answers and use them exactly as stated and whoever grades your test will love you.

Register for the October 5, 2020 SAT ASAP!

The October SAT is one of the three tests per year where you can select the “Question and Answer Service” (QAS). For an additional $18 you get to see a complete copy of the actual test as well as your answers. This can be really helpful for reviewing and eliminating mistakes. Got questions about the SAT? Our SAT FAQ page is packed with valuable information.

Make sure to select this option during the registration process:

Spend the extra $18 and get a full copy of the test!

My son Carter is just in 9th grade, but he will be taking the October test as a diagnostic check-up and a chance for me to analyze the latest trends in the test questions.

Make sure to register ASAP because registration after Sept. 6th requires paying the “Late Registration Fee.”

You can register for the test here.

More Free Official SAT Sample Tests

The College Board has recently released two more free sample tests on their website. Now there are 10 free practices tests available online!

We have all of the math sections available on this page.

The topic of Standard Deviation is starting to appear on the test more and more. It does not appear often, but it was not on any of the original 8 practice tests. Because most students have not taken statistics, this is a way to help those that have as well as help many students learn something new. If you do not know what Standard Deviation is, think of it as a measure of variability in data. If a stock price changes by a tiny bit here and there then it has a small standard deviation, but if a stock price changes frequently and has wild ups and downs then it has a large standard deviation. Alternatively, you could think of standard deviation as a way of measuring how thrilling a roller coaster is; a kiddie coaster has a small standard deviation while a full size roller coaster has a large standard deviation.

As always, a student’s success is determined by their long-term understanding of math and the work they have put in during their entire education, so we recommend studying hard every day in school and then doing dedicated test prep of 10-15 minutes per day (don’t miss any days!!) over an 8-10 week span to do your best on the SAT. With 10 free practice tests, that is enough to keep you practicing for about 45 days!

Our New Storefront for 2019!

Transformative Tutoring in Osprey, FL

We had a wonderful 2018-2019 school year and we are excited to make a difference in the community again this year. We had so many success stories and helped transform so many students last year! We know 2019-2020 will be even more amazing for our families! We recognize that the success of our students not only changed their lives, but changed the dynamics of their families. We received many reports of improved relationships and reduced stress and we are hoping to build on that success in the years to come. If your family is having math problems, come see us and experience the transformation.

Top 10 Questions To Do Together

In my years of teaching and tutoring, I have helped hundreds of students. Some had small problems they needed help with while others were basically starting from scratch. At Transformative Tutoring, we believe that every parent should spend a little time doing math with their child. Sure, your child gets a grade at the end of each year and perhaps has to pass an EOC exam, but what does that all mean?

Understanding Grades and SAT or ACT Scores

The best way to understand what that letter grade or SAT/ACT score means is to spend a little time actually having your child do some math with you. You might be surprised to find out that your teenager, who got just a B in Algebra 2, Precalculus or Calculus, is still adding and subtracting by counting on their fingers. (I would estimate that over 20% of high school students that have completed Algebra 2 still count on their fingers when not allowed to use a calculator.)

Students Are Growing Up in a Cashless, Digital World

Today’s children, in fact all of us, live in a digital age. Most middle class children rarely use coins and bills the way we did when we grew up. We had to know that four quarters made a dollar, but today’s children cannot buy anything with a quarter, so they don’t really care about quarters. Today’s children might have digital currency such as gift cards, debit cards, prepaid cards or iTunes credits, but they rarely handle cash. As a result, they use math for about 45 minutes a day about 180 days a year, exclusively in math class.

Compounding the problem for this digital generation is that calculators can do all their dirty work. In fact, you don’t even have to have a calculator anymore, just ask your smartphone something like, “Hey Siri, what’s 315 divided by 3.875?” As soon as most children find these error-free paths of least resistance they (ab)use them and shut their brains off entirely to the world of math. Before you know it, math doesn’t make any sense to them and they become incapable of thinking mathematically.

Beware of the Tools for Avoiding Math Homework

When a struggling math student hits high school there is often no easy way out and their struggles worsen. Did you know that every answer to every math textbook problem is available online? Most high school kids do! Now, they can breeze through their homework using sites like Slader, which has used crowd-sourcing to categorize every problem and answer, often with full solutions so students can “show their work.” Textbook publishers have tried to stay one step ahead by creating online homework assignments where the problems insert randomized numbers so that no two students get exactly the same question. However, in the great arms race to avoid doing math homework, once again there was a counter-attack in the form of an app called PhotoMath. Simply take a picture of any math problem and it will solve it for you, no thinking required! I have even heard reports of students using this app in their classroom to cheat on tests!

The SAT has a No Calculator Section

Eventually, the day of reckoning for all college bound students arrives, and that is the day of the SAT or ACT. These tests require students to know what they are doing and to actually understand and apply the math skills, formulas, strategies and concepts that they have, or haven’t, been using all of these years. Sadly, the arrival of that first SAT or ACT score is often the first day that a parent actually becomes aware of the magnitude of their child’s struggles with math. Now, they have a big problem on their hands, not much time to fix it and a jam packed schedule. Yes, there were B’s (many teachers require a student to be completely incompetent AND disrespectful to get a C grade these days, so a B should be considered a serious warning sign, especially if your child is well liked by their teachers) along the way that tried to serve as warning signs. Yes, there were some below average PSAT, PSAT 8/9, or EOC scores that tried to be the harbinger of the peril ahead, but these signs often were not obvious enough to raise enough concern to cause someone to take action.

Spend 5 Minutes Doing Math Together

So, today, and for the next few days, I beg you to sit down and spend a few minutes doing these problems with your child and without a calculator (20 of the 58 SAT math questions do not allow a calculator, while all 60 of the ACT math questions do allow a calculator) and see with your own eyes if your child needs help with arithmetic, Algebra 1, Geometry or Algebra 2.

ACT Score Percentiles

ACT Scores as Percentiles
ACT Score Percentiles

This table shows how your ACT score will rank you against your peers. It makes sense that a 36 would put you at the top with 100%, but it is interesting to see that a math score of 34 or 35 scores you at 99% and a score of 30 puts you in the top 95%! So, if you have scored 30 or above you have probably already scored well enough to impress most colleges.

While scores of 30-36 are nearly all the same percentile, it is a huge jump to change your score from a 20 to a 28! Making such a large improvement is equivalent to moving from the 55th percentile to the 91st percentile! So, set reasonable expectations. Do you really expect to move from the middle of the pack at 55% to the top 10% by studying just a couple hours? It will take LOTS of practice and probably lots of tutoring to make a large improvement like that, so set aggressive, yet realistic goals and work harder (LOTS of practice) and smarter (get some tutoring) to achieve them.

Raw Score to ACT Score Conversion

ACT Raw Score to Scaled Score Conversion
Raw Score to ACT Score Conversion Table

This table shows the number of correct answers required to earn a specific ACT score. For example, to get a score of 30 on the math test you must get 50 or 51 of the 60 questions correct.

It is hard to improve from a 19 to a 26 because you have to improve your raw score from 27/60 to 40/60. So, a 7 point ACT score improvement can require 13 more correct answers, which would be approximately a 50% improvement on the previous score! Because it is so hard to improve your score, make sure you do LOTS of practice and get some tutoring.